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A square matrix A is called orthogonal i...

A square matrix A is called orthogonal if.

A

`A'=A^(2)`

B

`A'=A^(-1)`

C

`A=A^(-1)`

D

`A'=A`

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A square matrix A is said to be orthogonal if A^T A=I If A is a sqaure matrix of order n and k is a scalar, then |kA|=K^n |A| Also |A^T|=|A| and for any two square matrix A d B of same order \AB|=|A||B| On the basis of abov einformation answer the following question: If A is an orthogonal matrix then (A) A^T is an orthogonal matrix but A^-1 is not an orthogonal matrix (B) A^T is not an orthogonal mastrix but A^-1 is an orthogonal matrix (C) Neither A^T nor A^-1 is an orthogonal matrix (D) Both A^T and A^-1 are orthogonal matices.

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Knowledge Check

  • If nth-order square matrix A is a orthogonal, then |"adj (adj A)"| is

    A
    always -1 if n is even
    B
    always 1 if n is odd
    C
    always 1
    D
    none of these

  • If a square matrix A is orthogonal as well as symmetric, then

    A
    A is involutory matrix
    B
    A is idempotent matrix
    C
    A is a diagonal matrix
    D
    none of these

  • A square matrix B is said to be an orthogonal matrix of order n if BB^(T)=I_(n) if n^(th) order square matrix A is orthogonal, then |adj(adjA)| is

    A
    may be `-1` if `n` is even
    B
    greater than `1` in all cases
    C
    always `1`
    D
    always 1 if `n` is odd

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